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Volumn 10, Issue 3, 2000, Pages 333-354

Target patterns and spirals in planar reaction-diffusion systems

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EID: 0038090708     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329910013     Document Type: Article
Times cited : (33)

References (40)
  • 1
    • 35949007726 scopus 로고
    • Stability limits of spirals and traveling waves in nonequilibrium media
    • I. S. Aranson, L. Aranson, L. Kramer, and A. Weber. Stability limits of spirals and traveling waves in nonequilibrium media, Phys. Rev. A 46 (1992) R2992-2995.
    • (1992) Phys. Rev. A , vol.46
    • Aranson, I.S.1    Aranson, L.2    Kramer, L.3    Weber, A.4
  • 2
    • 0040364533 scopus 로고
    • Bifurcation analysis of reaction-diffusion equations V. Rotating waves on a disk
    • Partial Differential Equations and Dynamical Systems (W. E. Fitzgibbon III, ed.) Pitman Press, Boston
    • G. Auchmuty. Bifurcation analysis of reaction-diffusion equations V. Rotating waves on a disk. In Partial Differential Equations and Dynamical Systems (W. E. Fitzgibbon III, ed.) Res. Notes Math. 101, Pitman Press, Boston, 1984, 35-63.
    • (1984) Res. Notes Math. , vol.101 , pp. 35-63
    • Auchmuty, G.1
  • 3
    • 0000535780 scopus 로고    scopus 로고
    • Space-time evolution of plasma instabilities - Absolute and convective
    • (M. N. Rosenbluth and R. Z. Sagdeev, eds.), North-Holland, Amsterdam
    • A. Bers. Space-time evolution of plasma instabilities - Absolute and convective. In Handbook of Plasma Physics (M. N. Rosenbluth and R. Z. Sagdeev, eds.), vol. 1, North-Holland, Amsterdam, pp. 451-517.
    • Handbook of Plasma Physics , vol.1 , pp. 451-517
    • Bers, A.1
  • 6
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. Cross and P. C. Hohenberg. Pattern formation outside of equilibrium, Rev. Mod. Phys. 65 (1993) 851-1112.
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 8
    • 0039179935 scopus 로고
    • Ferroin-collodion membranes: Dynamic concentration patterns in planar membranes
    • J. A. DeSimone, D. L. Beil, and L. E. Scriven. Ferroin-collodion membranes: Dynamic concentration patterns in planar membranes. Science 180 (1973) 946-948.
    • (1973) Science , vol.180 , pp. 946-948
    • Desimone, J.A.1    Beil, D.L.2    Scriven, L.E.3
  • 9
    • 58149210857 scopus 로고
    • Spatiotemporal selforganization on isothermal catalysts
    • M. Eiswirth, M. Bär, and H. H. Rotermund. Spatiotemporal selforganization on isothermal catalysts, Physica D 84 (1995) 40-57.
    • (1995) Physica D , vol.84 , pp. 40-57
    • Eiswirth, M.1    Bär, M.2    Rotermund, H.H.3
  • 10
    • 0019913660 scopus 로고
    • Internal waves in a contained rotating stratified fluid
    • S. Friedlander and W. L. Siegmann, Internal waves in a contained rotating stratified fluid, J. Fluid Mech. 114 (1982) 123-156.
    • (1982) J. Fluid Mech. , vol.114 , pp. 123-156
    • Friedlander, S.1    Siegmann, W.L.2
  • 11
    • 0027492193 scopus 로고
    • Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers
    • H. F. Goldstein, E. Knobloch, I. Mercader, and M. Net. Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers. J. Fluid Mech. 248 (1993) 583-604.
    • (1993) J. Fluid Mech. , vol.248 , pp. 583-604
    • Goldstein, H.F.1    Knobloch, E.2    Mercader, I.3    Net, M.4
  • 12
    • 85037513472 scopus 로고    scopus 로고
    • Hopf bifurcation from rotating waves and patterns in physical space
    • To appear
    • M. Golubitsky, V. G. LeBlanc, and I. Melbourne. Hopf bifurcation from rotating waves and patterns in physical space, J. Nonlin. Sci. To appear.
    • J. Nonlin. Sci.
    • Golubitsky, M.1    LeBlanc, V.G.2    Melbourne, I.3
  • 14
    • 0013198426 scopus 로고
    • Springer-Verlag, New York
    • M. Golubitsky, I. N. Stewart, and D. G. Schaeffer. Singularities and Groups in Bifurcation Theory, vol. 2. Applied Mathematical Sciences 69, Springer-Verlag, New York, 1988.
    • (1988) Applied Mathematical Sciences , vol.69
  • 15
    • 84867726599 scopus 로고
    • Experimental observations of ordered states of cellular flames
    • M. Gorman, M. el-Hamdi, and K. A. Robbins. Experimental observations of ordered states of cellular flames, Comb. Sci. & Tech. 98 (1994) 37-45.
    • (1994) Comb. Sci. & Tech. , vol.98 , pp. 37-45
    • Gorman, M.1    El-Hamdi, M.2    Robbins, K.A.3
  • 16
    • 0040958700 scopus 로고
    • Axi-symmetric, time-periodic solutions to λ-ω systems
    • J. Greenberg. Axi-symmetric, time-periodic solutions to λ-ω systems, SIAM J. Appl. Math. 34 (1978) 391-397.
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 391-397
    • Greenberg, J.1
  • 17
    • 0001645343 scopus 로고
    • Spiral waves in reaction-diffusion equations
    • P. Hagan. Spiral waves in reaction-diffusion equations, SIAM J. Appl. Math. 42 (1982) 762-786.
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 762-786
    • Hagan, P.1
  • 19
    • 11944258694 scopus 로고
    • Local and global instabilities in spatially developing flows
    • P. Huerre and P. A. Monkewitz. Local and global instabilities in spatially developing flows, Ann. Rev. Fluid Mech. 22 (1990) 473-537.
    • (1990) Ann. Rev. Fluid Mech. , vol.22 , pp. 473-537
    • Huerre, P.1    Monkewitz, P.A.2
  • 20
    • 0000039189 scopus 로고
    • A survey of spiral-wave behaviors in the Oregonator model
    • W. Jahnke and A. T. Winfree. A survey of spiral-wave behaviors in the Oregonator model, Intern. J. Bifur. & Chaos 1 (1991) 445-466.
    • (1991) Intern. J. Bifur. & Chaos , vol.1 , pp. 445-466
    • Jahnke, W.1    Winfree, A.T.2
  • 22
    • 0000723046 scopus 로고
    • Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension
    • N. Kopell and L. N. Howard. Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension. Advances in Appl. Math. 2 (1981) 417-449.
    • (1981) Advances in Appl. Math. , vol.2 , pp. 417-449
    • Kopell, N.1    Howard, L.N.2
  • 23
    • 0013033063 scopus 로고
    • The Ginzburg-Landau approach to oscillatory media
    • L. Kramer, F. Hynne, P. Graae Soerenson, and D. Walgraef. The Ginzburg-Landau approach to oscillatory media, Chaos 4 (1994) 443-452.
    • (1994) Chaos , vol.4 , pp. 443-452
    • Kramer, L.1    Hynne, F.2    Soerenson, P.G.3    Walgraef, D.4
  • 24
    • 0040958704 scopus 로고
    • Binary fluid convection in a cylinder
    • I. Mercader, M. Net, and E. Knobloch. Binary fluid convection in a cylinder, Phys. Rev. E 51 (1995) 339-350.
    • (1995) Phys. Rev. E , vol.51 , pp. 339-350
    • Mercader, I.1    Net, M.2    Knobloch, E.3
  • 25
    • 0001615127 scopus 로고
    • The structure of the core of the spiral wave in the Belousov-Zhabotinskii reaction
    • S. C. Müller, T. Plesser, and B. Hess. The structure of the core of the spiral wave in the Belousov-Zhabotinskii reaction, Science 240 (1985) 661-663.
    • (1985) Science , vol.240 , pp. 661-663
    • Müller, S.C.1    Plesser, T.2    Hess, B.3
  • 26
    • 45949121684 scopus 로고
    • Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction
    • S. C. Müller, T. Plesser, and B. Hess. Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction. Physica D 24 (1987) 71-86.
    • (1987) Physica D , vol.24 , pp. 71-86
    • Müller, S.C.1    Plesser, T.2    Hess, B.3
  • 27
    • 0003355611 scopus 로고
    • Mathematical Biology
    • Springer-Verlag, New York
    • J. D. Murray. Mathematical Biology. Biomath. 19, Springer-Verlag, New York, 1989.
    • (1989) Biomath. , vol.19
    • Murray, J.D.1
  • 28
    • 0002400305 scopus 로고
    • Attraction and adhesion in the slime mold Dictyostelium
    • Fungal Differentiation: A Contemporary Synthesis, J. E. Smith (ed), Marcel Dekker, New York
    • P. C. Newell. Attraction and adhesion in the slime mold Dictyostelium. In Fungal Differentiation: A Contemporary Synthesis, J. E. Smith (ed), Mycology Series 43, Marcel Dekker, New York (1983) 43-71.
    • (1983) Mycology Series , vol.43 , pp. 43-71
    • Newell, P.C.1
  • 29
    • 0000771172 scopus 로고    scopus 로고
    • Alternative scenarios of spiral breakup in a reaction-diffusion model with excitable and oscillatory dynamics
    • M. Bär and M. Or-Guil. Alternative scenarios of spiral breakup in a reaction-diffusion model with excitable and oscillatory dynamics, Phys. Rev. Lett. 82 (1999) 1160-1163.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1160-1163
    • Bär, M.1    Or-Guil, M.2
  • 30
    • 0242449865 scopus 로고    scopus 로고
    • Cellular pattern formation in circular domains
    • A. Palacios, G. H. Gunaratne, M. Gorman, and K. A. Robbins. Cellular pattern formation in circular domains. Chaos 7 (1997) 463-475.
    • (1997) Chaos , vol.7 , pp. 463-475
    • Palacios, A.1    Gunaratne, G.H.2    Gorman, M.3    Robbins, K.A.4
  • 31
    • 0032361995 scopus 로고    scopus 로고
    • Bifurcation to spiral waves in reaction-diffusion systems
    • A. Scheel. Bifurcation to spiral waves in reaction-diffusion systems, SIAM J. Math. Anal. 29 (1998) 1399-1418.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1399-1418
    • Scheel, A.1
  • 32
    • 0031260793 scopus 로고    scopus 로고
    • Subcritical bifurcation to infinitely many rotating waves
    • A. Scheel. Subcritical bifurcation to infinitely many rotating waves, J. Math. Anal. Appl. 215 (1997) 252-261.
    • (1997) J. Math. Anal. Appl. , vol.215 , pp. 252-261
    • Scheel, A.1
  • 33
    • 44049111811 scopus 로고
    • Chemical spiral rotation is controlled by light-induced artificial cores
    • O. Steinbock and S. C. Müller. Chemical spiral rotation is controlled by light-induced artificial cores, Physica A 188 (1992) 61-67.
    • (1992) Physica A , vol.188 , pp. 61-67
    • Steinbock, O.1    Müller, S.C.2
  • 34
    • 0000003620 scopus 로고    scopus 로고
    • On the breakup of spiral waves into chemical turbulence
    • S. M. Tobias and E. Knobloch. On the breakup of spiral waves into chemical turbulence, Phys. Rev. Lett. 80 (1998) 4811-4814.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 4811-4814
    • Tobias, S.M.1    Knobloch, E.2
  • 35
    • 22244448107 scopus 로고    scopus 로고
    • Convective and absolute instabilities of fluid flows in finite geometry
    • S. M. Tobias, M. R. E. Proctor, and E. Knobloch. Convective and absolute instabilities of fluid flows in finite geometry, Physica D 113 (1998) 43-72.
    • (1998) Physica D , vol.113 , pp. 43-72
    • Tobias, S.M.1    Proctor, M.R.E.2    Knobloch, E.3
  • 36
    • 0032003354 scopus 로고    scopus 로고
    • Periodic, aperiodic, and transient patterns in vibrated granular layers
    • P. B. Umbanhowar, F. Melo, and H. L. Swinney. Periodic, aperiodic, and transient patterns in vibrated granular layers, Physica A 249 (1998) 1-9.
    • (1998) Physica A , vol.249 , pp. 1-9
    • Umbanhowar, P.B.1    Melo, F.2    Swinney, H.L.3
  • 38
    • 0001899647 scopus 로고
    • Rotating chemical reactions
    • June
    • A. T. Winfree. Rotating chemical reactions, Scientific American, June 1974, 82-95.
    • (1974) Scientific American , pp. 82-95
    • Winfree, A.T.1
  • 39
    • 0001928973 scopus 로고    scopus 로고
    • Focus Issue: Fibrilation in Normal Ventricular Myocardium
    • A. T. Winfree (ed.), Focus Issue: Fibrilation in Normal Ventricular Myocardium, Chaos 8 (1998).
    • (1998) Chaos , vol.8
    • Winfree, A.T.1
  • 40
    • 0030258439 scopus 로고    scopus 로고
    • Spiral waves on circular and spherical domains of excitable medium
    • V. S. Zykov and S. C. Müller. Spiral waves on circular and spherical domains of excitable medium, Physica D 97 (1996) 322-332.
    • (1996) Physica D , vol.97 , pp. 322-332
    • Zykov, V.S.1    Müller, S.C.2


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